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Programming an algebraic experiment

• To: mathgroup at smc.vnet.net
• Subject: [mg34687] Programming an algebraic experiment
• From: riefler at iwt.uni-bremen.de
• Date: Sat, 1 Jun 2002 04:28:47 -0400 (EDT)
• Organization: Universitaet Bremen, Germany
• Sender: owner-wri-mathgroup at wolfram.com

Hi

Given 4 complex numbers S1, S2, S3 and S4 with Si = xi + i*yi,
i=1,2,3,4.

These 4 numbers are the basis for the following 16 eqn.s:

S11 = 1/2 * ( abs(S1)^2 + abs(S2)^2 + abs(S3)^2 + abs(S4)^2 );
S12 = 1/2 * ( - abs(S1)^2 + abs(S2)^2 - abs(S3)^2 + abs(S4)^2 );
S13 = real( S2*conj(S3) + S1*conj(S4) );
S14 = imag( S2*conj(S3) - S1*conj(S4) );
S21 = 1/2 * ( - abs(S1)^2 + abs(S2)^2 + abs(S3)^2 - abs(S4)^2  );
S22 = 1/2 * (  abs(S1)^2 + abs(S2)^2 - abs(S3)^2 - abs(S4)^2 );
S23 = real( S2*conj(S3) - S1*conj(S4) );
S24 = imag( S2*conj(S3) + S1*conj(S4) );
S31 = real( S2*conj(S4) + S1*conj(S3) );
S32 = imag( S2*conj(S4) - S1*conj(S3) );
S33 = real( S1*conj(S2) + S3*conj(S4) );
S34 = imag( conj(S1)*S2 + conj(S3)*S4 );
S41 = imag( conj(S2)*S4 + S1*conj(S3) );
S42 = imag( conj(S2)*S4 - S1*conj(S3) );
S43 = imag( S1*conj(S2) - S3*conj(S4) );
S44 = real( S1*conj(S2) - S3*conj(S4) );

"abs" stands for the absolute value and "conj" for the complex
conjugate value of the Si.

Now my aim is to find any combination - independent how long - with
and between these Sii to get the following result:

              K=y1+y2

Now my question to you is:
How can I instruct Mathematica that it will look for an answer?

I want to see Mathematica that it is carried out as much as possible
combinations, simplify these combinations algeabraically and then
compare the simplified solution with K.

Thank you

Norbert